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A critical examination of Allen’s theory of action and time. (English) Zbl 0733.03017
Author’s abstract: “J.F. Allen’s theory of time and action is examined and found to be unsuitable for representing facts about continuous change. A series of revisions to Allen’s theory is proposed in order to accommodate this possibility. The principal revision is a diversification of the temporal ontology to include instants on the same footing as intervals; a distinction is also made between two kinds of properties, called states of position and states of motion, with respect to the logic of their temporal incidence. As a consequence of these revisions, it is also found necessary to diversify the range of predicates specifying temporal location. Finally, it is argued that Allen’s category of processes is superfluous, since it can be assimilated with the category of properties. The implications of this assimilation for the representation of sentences containing verbs in the progressive aspect are discussed.”
Reviewer’s comment: Hans Kamp has also considered a logic of intervals (this goes back to N. Wiener, at the beginning of the century) in his work on DRT.

MSC:
03B60 Other nonclassical logic
68T27 Logic in artificial intelligence
68T30 Knowledge representation
03B80 Other applications of logic
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